# Exponential shortcut to measurement-induced entanglement phase transitions

## TL;DR

This paper introduces a scalable method using fluctuations of a few qubits to experimentally detect measurement-induced entanglement phase transitions, bypassing the need for exponential measurements of entanglement entropy.

## Contribution

The authors propose a novel, efficient approach to observe entanglement phase transitions via fluctuations, applicable even with conserved quantities, simplifying experimental detection.

## Key findings

- Fluctuations can reveal entanglement phase transitions.
- The method requires measuring only a few qubits.
- It provides a scalable alternative to entropy measurements.

## Abstract

Recently discovered measurement-induced entanglement phase transitions in monitored quantum circuits provide a novel example of far-from-equilibrium quantum criticality. Here, we propose a highly efficient strategy for experimentally accessing these transitions through fluctuations. Instead of directly measuring entanglement entropy, which requires an exponential number of measurements in the subsystem size, our method provides a scalable approach to entanglement transitions in the presence of conserved quantities. In analogy to entanglement entropy and mutual information, we illustrate how bipartite and multipartite fluctuations can both be employed to analyze the measurement-induced criticality. Remarkably, the phase transition can be revealed by measuring fluctuations of only a handful of qubits.